Scalar Flux–Gradient Relationships Under Unstable Conditions over Water in Coastal Regions

Abstract

The scalar flux–gradient relationships of temperature ( $$\phi _{T}$$ ) and specific humidity ( $$\phi _{q}$$ ) under unstable conditions are investigated using eddy-covariance measurements of air–sea turbulent fluxes and vertical profiles of temperature and specific humidity collected from a marine meteorological platform. The gradients of temperature and specific humidity are obtained from measurements at five heights above the sea surface using the log-square fitting method and the simpler first-order approximation method. The two methods yield similar results. The proposed flux–gradient relationships $$\phi _{T}$$ and $$\phi _{q}$$ covers a wide range of instability: the stability parameter $$\zeta $$ ranges from $$-$$ 0.1 to $$-$$ 50. The functional form of the proposed flux–gradient relationships is an interpolation between the Businger–Dyer relation and the free convection relation, which includes the “ $$-$$ 1/2” and “ $$-$$ 1/3” scaling laws at two different stability regimes. The widely used COARE 3.0 algorithm, which is an interpolation between the integrals of the Businger–Dyer and the free convection relations, is also evaluated and compared. The analysis and comparisons show that both schemes generate reasonable values of $$\phi _{q}$$ in the whole unstable regime. The COARE 3.0 algorithm, however, overestimates $$\phi _{T}$$ values under very unstable conditions. The errors in the flux–gradient relationships induced by the random errors in the turbulence measurements are assessed. When the random errors are taken into account, the observations agree with predictions of various schemes fairly well, implying that the dominant transport mechanism is adequately captured by the Monin–Obukhov similarity theory. The study also shows that $$\phi _{q}$$ is significantly $${>}\phi _{T}$$ under unstable conditions and that the ratio $$\phi _{q}/\phi _{T}$$ increases with $$-\zeta $$ . The ratio of $$\phi _{q}$$ to $$\phi _{T}$$ and the ratio of turbulent transport efficiencies of heat and water vapour ( $$R_{wT}/R_{wq}$$ ) suggest that heat is transported more efficiently than water vapour under unstable conditions.